A Categorical Framework for the Quantum Harmonic Oscillator |
| |
Authors: | Jamie Vicary |
| |
Institution: | (1) Imperial College London, London, UK |
| |
Abstract: | This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction
of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an entirely
general one in which Hilbert spaces play no special role.
Generalised coherent states arise through the hom-set isomorphisms defining the adjunction, and we prove that they are eigenstates
of the lowering operators. Generalised exponentials also emerge naturally in this setting, and we demonstrate that coherent
states are produced by the exponential of a raising morphism acting on the zero-particle state. Finally, we examine all of
these constructions in a suitable category of Hilbert spaces, and find that they reproduce the conventional mathematical structures. |
| |
Keywords: | Quantum Category Fock space Canonical commutation relations Harmonic oscillator |
本文献已被 SpringerLink 等数据库收录! |
|